Thursday, February 1, 2018

Muon g-2 Anomaly Fully Explained With General Relativity? UPDATED

I just learned some interesting news from Tommaso Dorigo’s blog. Go there for more details, but the news is the claim in thesethreepapers that, accounting for GR effects on the precision measurement of the muon anomalous magnetic moment, the three sigma difference between experiment and theory goes away.

This sort of calculation needs to be checked by other experts in the field, and provides an excellent example of where you want good peer review. Presumably we’ll hear fairly soon whether the result holds up (the papers are not long or complicated). If this is right, it’s a fantastic example of our understanding of fundamental physics at work, with the muon g-2 experiments measuring something they weren’t even looking for, a subtle effect of general relativity. . . .

The significance of this is that (setting aside questions about the neutrino sector), the muon g-2 measurement is the most prominent one I’m aware of where there has been a serious (three sigma) difference between experiment and Standard Model theory. This has often been interpreted as evidence for SUSY extensions of the SM. Projects producing “fits” that “predict” SUSY particles with masses somewhat too high to have been seen yet at the LHC use the g-2 anomaly as input.

The money language at Dorigo's blog (Quantum Diary Survivor) is as follows:

[The three preprints published today] consider gravitational effects due to the Earth on the magnetic moment of the electron and the muon. The effect of the curvature of spacetime is of two parts in a billion, and should be the same for all fermions. The authors computed the effect, finding that for the electron the modification can be reabsorbed in the calculation, while for the muon a modification arises. The difference has roots in the fact that the measurement in the muon case is made in a highly relativistic regime.

It all boils down to this: if the three theorists will be shown to have made no mistake in their calculation, the infamous "G-2 anomaly" of the magnetic muon moment will exist no more. The idea that classical gravitational effects affect its value in a way quite consistent with the observed departure is extremely surprising and exhilarating, if you ask me. . . .

What I would like to see now, however, is a set of phenomenological papers that recompute the favourite space of SUSY instantiations under the hypothesis that the muon G-2 is exactly at its SM expectation.

With the correction the difference between the theoretical calculation and the experimental value is less than one sigma (with all of the change coming on the theoretical value side).

Lubos also wrote a post on the papers and is generally upbeat about their prospects for being correct, although he acknowledges not yet having read the papers closely. (UPDATE and shows disdain for them in a later post.)

If true, this is huge.

Why?

Muon g-2 is sensitive globally to any discrepancies in the particle spectrum between the Standard Model and reality, to many, many significant digits. At a minimum an absence of a muon g-2 anomaly insures that there is a large "desert" between the energy scale of the top quark and Higgs vev (173 GeV and 246 GeV respectively) and any "new physics" beyond the Standard Model.

Put another way, it would almost insure that a next generation particle collider will find no new physics.

I've read a paper or two strongly suggesting that the anomalous proton radius in muonic hydrogen similarly arises from a failure to properly use consistent special and/or general relativity frames of reference in the calculations involved.

It would also represent significant progress more generally in integrating the Standard Model and General Relativity, not by inventing a theory of quantum gravity, but simply by finding an ad hoc way to incorporate General Relativity into Standard Model physics calculations, even though the two Core Theories of physics are fundamentally incompatible with each other if taken to extremes.

The papers and their abstracts outlining the analysis are below the fold.

UPDATE February 5, 2018.

A short new pre-print from a Wellington, New Zealand based physicist posted three days after the original papers concludes that these papers are flawed:

In three very recent papers, (an initial paper by Morishima and Futamase, and two subsequent papers by Morishima, Futamase, and Shimizu), it has been argued that the observed experimental anomaly in the anomalous magnetic moment of the muon might be explained using general relativity. It is my melancholy duty to report that these articles are fundamentally flawed in that they fail to correctly implement the Einstein equivalence principle of general relativity. Insofar as one accepts the underlying logic behind these calculations (and so rejects general relativity) the claimed effect due to the Earth's gravity will be swamped by the effect due to Sun (by a factor of fifteen), and by the effect due to the Galaxy (by a factor of two thousand). In contrast, insofar as one accepts general relativity, then the claimed effect will be suppressed by an extra factor of [(size of laboratory)/(radius of Earth)]^2. Either way, the claimed effect is not compatible with explaining the observed experimental anomaly in the anomalous magnetic moment of the muon.

The response from the g-2 collaboration (from the spokesperson Chris Polly):

Our spokes already replied to the authors since they made a mistake in the final conclusion. While the additional effect in the bxE term they calculate is 2ppm, they then attribute this full term to be the change in g-2. However, they forgot that that additional contribution needs to be weighted by the relative strength of the bxE term which is 1330ppm of the B field. So even if their calculation was correct, the actual contribution is 2ppm*1330ppm=2ppb. That’s negligible for the ongoing experiments measuring to ~100ppb precision. And this argument does not even involve any judgement on the validity of the additional term they calculate.

Regardless of whether or not the GR is correct, the authors make an error at the end of their paper by failing to take the relative strengths of the E and B fields used by the experiment into account. The vast majority of the muon precession is driven by the B-field while the E-field is only a small perturbation. The maximum E-field experienced by a muon in the g-2 storage ring is 30kV/5cm while the B-field is 1.5T. That means betaXE is very small compared to B...to be precise betaXE is 1300 parts per million (ppm) compared to B. So, in their treatment they find an additional modification to the coefficient in front of the betaXE term that shifts the value of the coefficient by 2ppm. Therefore, the overall impact on the anomalous magnetic moment extracted by the experiment would change by 2ppm x 1300 ppm = 2.7 parts per billion (ppb), which is well below the 500ppb error on the BNL experiment and the 140ppb error targeted at Fermilab. This is actually an overestimate since we used the maximum E-field a muon can experience in the g-2 ring in the calculation. If you cannot find anywhere in the paper where they state the average magnitudes of E and B observed by muons in the experiment, then you know there is a problem. For instance, they would find the same correction arising from the betaXE term would apply to the experiment proposed at J-PARC even though the novel design of that experiment has E=0 by construction.

There also also many comments in the cited blog posts and some updates to their body texts.

The magnetic moment of free fermions in the curved spacetime has been studied based on the general relativity. Adopting the Schwarzschild metric for the background spacetime, the effective value of the magnetic moment has been calculated up to the post-Newtonian order O(1/c2) for three cases (A) Dirac particles with g=2, (B) neutral fermions with g≠2 and e=0 and (C) charged fermions with g≠2 and e≠0. The result shows their gravity dependence is given as μeffm=(1+3ϕ/c2)μm for all of these cases in which the coupling between fermions and the electromagnetic field is essentially different. It implies that the magnetic moment is influenced by the spacetime curvature on the basis of the general relativity commonly for point-like fermions, composite fermions and spread fermions dressed with the vacuum fluctuation. The gravitational effect affects the gyro-magnetic ratio and the anomalous magnetic moment as geff≃(1+3ϕ/c2)g, aeff≃a+3(1+a)ϕ/c2. Consequently, the anomalous magnetic moment of fermions with g≃2 measured on the Earth's surface contains the gravitational effect as |aeff|≃3|ϕ|/c2≃2.1×10−9, which implies that the gravitational anomaly of 2.1×10−9 is induced by the curvature of the spacetime on the basis of the general relativity in addition to the quantum radiative corrections for all fermions including electrons and muons.

The general relativistic effects to the anomalous magnetic moment of the electron ge-2 in the Earth's gravitational field have been examined. The magnetic moment of electrons to be measured on the Earth's surface is evaluated as μeffm≃(1+3ϕ/c2)μm on the basis of the Dirac equation containing the post-Newtonian effects of the general relativity for fermions moving in the Earth's gravitational field. This implies that the anomalous magnetic moment of 10−9 appears in addition to the radiative corrections in the quantum field theory. This may seem contradictory with the fact of the 12th digit agreement between the experimental value measured on the ground level ge(EXP) and the theoretical value calculated in the flat spacetime ge(SM). In this paper, we show that the apparent contradiction can be explained consistently with the framework of the general relativity.

The general relativistic effects to the anomalous magnetic moment of muons moving in the Earth's gravitational field have been examined. The Dirac equation generalized to include the general relativity suggests the magnetic moment of fermions measured on the ground level is influenced by the Earth's gravitational field as μeffm≃(1+3ϕ/c2)μm, where μm is the magnetic moment in the flat spacetime and ϕ=−GM/r is the Earth's gravitational potential. It implies that the muon anomalous magnetic moment measured on the Earth aμ≡gμ/2−1 contains the gravitational correction of |aμ|≃2.1×10−9 in addition to the quantum radiative corrections. The gravitationally induced anomaly may affect the comparison between the theoretical and experimental values recently reported: aμ(EXP)−aμ(SM)=28.8(8.0)×10−10(3.6σ). In this paper, the comparison between the theory and the experiment is examined by considering the influence of the spacetime curvature to the measurement on the muon gμ−2 experiment using the storage ring on the basis of the general relativity up to the post-Newtonian order of O(1/c2).

7 comments:

I imagine, also, if this pans out, then we can correct for Earth's gravity in experiments done here on Earth, and we won't have to build those next-generation colliders out in Trojan / Greek lagrange points in space.

I like your second idea better. In orbital muon g-2 experiment wouldn't be cheap, but it would be a lot cheaper than a next generation LHC or a moonshot or a manned trip to Mars, and the model independent scientific value of doing that would be greater that any of those more expensive options.

Not quite. Electromagnetism (i.e. QED) we have completely mastered. We have also pretty much mastered the weak force. And, this greatly reduces the likelihood that there are any new particles or forces to be discovered except at extremely high (maybe too high to study with experiments costing less than a trillion to ten trillion 2018 dollars) energy scales. (Muon g-2 is less sensitive to new particles many orders of magnitude higher than a top quark than it is to new particles that are lighter than that.) But, there are some areas that are still ripe for progress:

1. Neutrino physics. Topics include: determining the CP violating phase(s) of neutrion oscillations, determining the absolute neutrino mass, improving measurements of neutrino constants, understanding the mechanism by which neutrino mass arises (Dirac with or without the Higgs field or Majorana) which also governs the question of whether neutrinoless beta decay happens and if so how often, and the ratio of neutrinos to antineutrinoes in the universe.

2. QCD. The math in QCD (the strong force) is so hard that we can calculate very few things from first principles at more than 1% accuracy and there are quite a few kinds of composite particles made of quarks (scalar mesons, axial vector mesons, tetraquarks, pentaquarks, hexaquarks, glueballs) that naively should exist, but we don't understand well. We suspect that many composite particles bound by QCD are blends of different particles, but have very little good theory to explain why particles blend one way and not the other. We also haven't made much progress in understanding analytically and from first principles as opposed from big tables compiled from mountains of experimental evidence the "parton distribution function" which is a set of probabilities about certain kinds of particles turning into other kinds of particles under different conditions. Even in seemingly pure QED dominated phenomena like the muon g-2, most of the error comes from the tiny QCD contribution and not from the QED or weak force components of the calculation (or from gravity). The good news in QCD is that even if you don't make any breakthroughs analytically in how you solve QCD equations (and the reality is that we are making slow but steady progress there), you can also make meaningful incremental improvement by throwing more and faster computers at it. So, this is an area of science were simply spending more money pretty much guarantees some meaningful process. It is the theory side that is lagging because the math is so hard, not the experiment side.

3. Quantum gravity, dark matter, modified gravity, dark energy, and cosmological inflation. I lump these together because these are phenomena mostly studied through astronomy even though the have particle physics implications. This is pretty much the only area of physics where we can pretty much guaranteed that there is "beyond the Standard Model" and/or "beyond General Relativity" physics out there to be discovered, we just haven't figured out exactly what it is although we have some decedent phenomenological models. While most aspects of particle physics have a garden hose level of new data coming in, advances in space satellites, LIGO type gravity wave detectors, neutrino telescopes, and improvements in computational power conspire to make the volume of new astronomy data coming in more like Niagara Falls. So, here we have two great things - an area where spending more money is guaranteed to provide more data in useful quantities, and a guaranteed prize for whoever figures out the new physics between dark matter/dark energy/modified gravity. Also, the fact that progress is driven by new data rather that merely new ideas with the same old data, means that we won't see that stagnation we have in the last few decades of particle physics.

4. Within the Standard Model physics, GUTs, TOEs, and the like. The key here is really precision measurement. Nobody thinks that the two dozen or so constants in the Standard Model are really random, but nobody has come up with a convincing theory regarding how they are derived. One of the main parts of this problem is that the less precisely we know the physical constants, the easier it is to come up with a false theory to explain their values. One a percentage basis, the least accurately know constants are the light quark masses, the strong force coupling constant, a few neutrino physics constants and the gravitational force constant(s) are the least accurately known. We actually have quite precise measurements on a percentage basis of both the top quark mass (about 0.4%) and Higgs boson mass (0.2%), but because the absolute values of the uncertainties of in these constants is so great because they are two of the largest mass dimensioned constants in the Standard Model (although they are easy to conver to pure number "Yuakawas" that are equivalent), small percentage errors in these measurements still swamp experimental uncertainties in Standard Model constants from all other sources. The uncertainty in the top quark mass, which is by far the greatest in absolute value, is also going to be pretty resistant to more than marginal improvement for the short to medium term, while the Higgs boson mass measurement's precision can still improve quite a bit in the medium term simply by reducing statistical error by collecting more data in experiments with the current state of the art in systemic error. Supersymmetry looked like a promising angle for a long time in this arena, but in its naive and crude forms, it is increasingly clear that this is not the solution. Preon theories are tempting the the energy scale they have to operate on if the methodology of our experimental exclusions is right is extremely high. String theory has some really beautiful and powerful concepts, but taming it into a form that has some connection that has a connection to real life has been elusive for 40-50 years.